Calculate a Rating Change
How the Elo Rating System Works
The Elo rating system, created by physicist and chess master Arpad Elo, predicts the likely outcome of a game from two players' ratings and then adjusts both ratings based on what actually happened. If you're rated higher than your opponent, you're "expected" to score more than half a point on average — beating that expectation gains rating, falling short of it loses rating, regardless of whether you technically won or lost the game.
Expected score formula: for a player rated RA facing
an opponent rated RB, the expected score is
EA = 1 / (1 + 10(RB − RA)/400),
a number between 0 and 1. A 200-point rating edge corresponds to roughly a 76% expected score;
a 400-point edge to roughly 91%.
Rating change formula: your new rating is
RA' = RA + K × (SA − EA), where
SA is your actual score (1 for a win, 0.5 for a draw, 0 for a loss) and
K is the K-factor: a multiplier that controls how quickly ratings move.
What Is the K-Factor?
A higher K-factor means each game moves your rating more; a lower one means ratings are more stable and change more slowly. Federations and platforms don't all use the same value — FIDE uses a larger K-factor for new or lower-rated players (whose "true" strength is still uncertain) and a smaller one for established masters, on the reasoning that a strong, experienced player's rating should already be close to accurate and shouldn't swing wildly on one result. Most online chess sites simplify this to a single flat K-factor, commonly 32, regardless of rating.